The capacity of glass X is 80 percent of the capacity of

[M7MBA]

The capacity of glass X is 80 percent of the capacity of glass Y. Glass X contains how many more ounces of punch than glass Y?

(1) Glass X contains 6 ounces of punch and is half-full, while glass Y is full.
(2) Glass X is 70 percent full, and glass Y is 30 percent full.

The OA is A.

How can I solve this DS question? Can any expert explain to me this step by step? Thanks in advanced.

[ErikaPrepScholar]

Quick note: Statement 1 says the glass is full, while Statement 2 says the glass is 30% full, which means both statements can't be true at the same time. In a real GMAT problem or a high-quality practice problem, Statement 1 and Statement 2 MUST both be able to be true at the same time. This means that this problem is unrealistic and not great for practice. That said ...

We know from the question stem that the capacity of X is 80% the capacity of Y:
X = 0.8Y

We want to find the difference in the amount of *punch* (not capacity) between X and Y.

Statement 1
Glass X has 6 ounces of juice and is half full. This means that Glass X is only using half of its capacity, so the total capacity of Glass X is 6 * 2 = 12 ounces. Glass Y is full, which means it is using its full capacity. We can solve for the capacity of Y using our equation from the question stem and plugging in 12 ounces for the capacity of X:
X = 0.8Y
12 = 0.8Y
15 = Y

So there are 15 ounces of punch in Y and 6 ounces of punch in X, which is a 9 ounce difference. Sufficient.

Note again: the question stem indicates that glass X should have more punch than glass Y, which it does not. Another indication that this practice question isn't particularly high quality.

Statement 2
We know that glass X is 70% full (0.7X = 0.7(0.8Y) = 0.56Y), while glass Y is 30% full (0.3Y).

We know a lot about the relative volumes of punch and total capacities, but we have no concrete measurements anywhere. This means that glass X could be 8 ounces and glass Y could be 10 ounces, making the volume of punch in glass X 5.6 ounces and the volume of punch in glass Y 3 ounces. This would give a difference of 2.6 ounces. However, glass X could be 16 ounces and glass Y could be 20 ounces, making the volume of punch in glass X 11.2 ounces and the volume of punch in glass Y 6 ounces. This would give a difference of 5.2 ounces.

So we can't successfully determine the difference in amount of punch between glasses Y and X. Insufficient.

I'd recommend being more careful about selecting high-quality practice questions - official GMAT problems are your best bet, but some test prep companies (like PrepScholar) work really hard to ensure that their questions are accurate to the exam.